Homework Help:
Maximum Force Applied to Brakes

Suppose you are driving a light weight pickup truck, and it takes 15m of stopping distance to stop when you are traveling 5 m/s, using max. force from the brakes.

1. Suppose you really load up the truck, so that the mass of the loaded truck is twice that of the unloaded truck. How much distance will be required to stop then, starting from 5 m/s again. Justify your answer in writing.

2. Now the truck is unloaded again. How much distance will be needed to stop , again using max brake force, if you are moving at 15 m/s to begin with? Justify your answer in writing.

2. Relevant equations

W stopping, more = F brakes, max x d wheel rolls forward, more
F=ma

3. The attempt at a solution

When you apply the brakes in your automobile, I know that caliper ‘pinchers’ apply force to your (turning) wheels, which produces friction when the wheels and calipers rub each other. I know that this friction converts the KE of your moving car into heat energy. When all the KE energy is changed into heat, the car has stopped.

The ‘stopping work’, W stopping = F brakes x d wheel rolls forward .

I know there is a maximum to the force applied by your brake calipers, F max . More force not possible I guess. But you can do more work even if you have maxed out on force by the wheels rolling forward more, this increases the d distance. So, more stopping work gets done.

This is as far as I have gotten in regards to both problems. I am really just completely lost. Any help would be much appreciated.

Hi hbrinn, welcome to PF.
Maximum brake force is independent of mass of the truck and its velocity.
So 1/2*m*v^2 = F*d............(1)
Use this equation to solve the problem.
The distance moved by the truck before it comes to rest depends on the mass of the truck and its velocity.